Knowing the ground state energies of molecules and atoms gives scientists critical insight into these particles' behavior in reactions, thermodynamic and molecular properties, and excitation energies. However, due to the quantum mechanical nature of particles, finding the ground state of a system is intractable, both mathematically and experimentally. Computational methods are utilized to estimate the ground state energies. As we approach the limits of classical computers, quantum computers are viewed as promising alternatives that present a bright future for computational chemistry. In this paper, I review classical and quantum algorithms/methods for computational chemistry. Then, I discuss the current topics in using quantum computers for computational chemistry by analyzing the performance of the Variational Quantum Eigensolver (VQE) in different contexts on IBM's noisy quantum computer simulator, "QasmSimulator," and one of IBM's quantum computers, ibmq_belem. This review presents a theoretical and practical view of quantum computational chemistry. It allows the reader to learn the theory behind the algorithms and implement them with the guidance of the presented code and its detailed explanations. The purpose of this paper is to leave the reader with the necessary theory and adequate programming reference to implement the algorithms in various contexts. [ABSTRACT FROM AUTHOR]